Steiner’s formula in the Heisenberg group

Balogh, Zoltan; Ferrari, Fausto; Franchi, Bruno; Vecchi, Eugenio; Wildrick, Kevin Michael (2015). Steiner’s formula in the Heisenberg group. Nonlinear analysis: theory, methods & applications, 126, pp. 201-217. Elsevier 10.1016/j.na.2015.05.006

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Steiner’s tube formula states that the volume of an ϵ-neighborhood of a smooth regular domain in Rn is a polynomial of degree n in the variable ϵ whose coefficients are curvature integrals (also called quermassintegrals). We prove a similar result in the sub-Riemannian setting of the first Heisenberg group. In contrast to the Euclidean setting, we find that the volume of an ϵ-neighborhood with respect to the Heisenberg metric is an analytic function of ϵ that is generally not a polynomial. The coefficients of the series expansion can be explicitly written in terms of integrals of iteratively defined canonical polynomials of just five curvature terms.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Balogh, Zoltan; Franchi, Bruno; Vecchi, Eugenio and Wildrick, Kevin Michael

Subjects:

500 Science > 510 Mathematics

ISSN:

0362-546X

Publisher:

Elsevier

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

08 Jun 2016 16:07

Last Modified:

17 Apr 2018 09:39

Publisher DOI:

10.1016/j.na.2015.05.006

BORIS DOI:

10.7892/boris.81134

URI:

https://boris.unibe.ch/id/eprint/81134

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